A334162 a(0) = 1; thereafter a(n) = exp(-1/n) * Sum_{k>=0} (n*k + 1)^n / (n^k * k!).

1, 2, 6, 35, 352, 5307, 111592, 3117900, 111259904, 4912490375, 261954304224, 16560019685937, 1222893826048000, 104189533522270666, 10132262911996769408, 1114216450970154278543, 137427598621356912082944, 18877351974681584403701519, 2869969478954093766868948480

Offset: 0

Author

Ilya Gutkovskiy, Apr 16 2020

Keywords

• nonn

Links

• Moussa Benoumhani, On Whitney numbers of Dowling lattices, Discrete Math. 159 (1996), no. 1-3, 13-33.

Crossrefs

Cf. A000110, A007405, A003575, A003576, A003577, A003578, A003579, A003580, A003581, A003582, A301419, A334165.

Programs

Mathematica

Table[SeriesCoefficient[1/(1 - x) Sum[(x/(1 - x))^k/Product[(1 - n j x/(1 - x)), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 18}]
Join[{1}, Table[n! SeriesCoefficient[Exp[x + (Exp[n x] - 1)/n], {x, 0, n}], {n, 1, 18}]]

Formula

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (x/(1 - x))^k / Product_{j=1..k} (1 - n*j*x/(1 - x)).

a(n) = n! * [x^n] exp(x + (exp(n*x) - 1) / n), for n > 0.

a(n) = A334165(n,n).